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Is Time an Infinite Set of Moments?

November 9, 2015 Leave a comment Go to comments

…or is the whole notion of an infinite set a paradox?

Since a set is by definition a defining of a boundary, whenever we talk about sets which are infinite we are talking about a boundary containing unbounded contents. Such a boundary makes it necessary that boundary-making itself is presumed to be outside of things being bound, i.e. it is taken as axiomatic that boundary making is part of a theory which does not change anything except our own understanding.

Things get murky however, when we consider time an infinite set. In Zeno’s Paradox of the Tortoise and Achilles, for example, the idea of an infinite set is used to trick us into thinking that motion is impossible. The logic is that for something to move one unit of distance, it must first move an infinite number of smaller distances. We can reverse this logic, however, and say that to divide one distance into an infinite number of smaller distances in the first place would take an infinitely long time if we had to actually make those measurements in some way, provided each measurement takes a non-zero amount of time.

Here is the difference between the map and the territory. Actually moving across a distance is a ‘territory’; a concrete reality. The idea that there is some number of points in which could be measured along that distance is a theoretical abstraction. When we apply the abstraction of infinity to the reality of concrete phenomena, we get paradox. The tortoise’s lead appears to always be getting smaller and smaller, but is still a nonzero fraction of the total distance ahead of Achilles, no matter how much faster Achilles is. What distracts us is that we are taking our own measurement for granted. Yes, it’s true that each measurement at time t will find the tortoise ahead of Achilles if we keep giving the tortoise a fraction of his original head start after calculating Achilles position, but infinity doesn’t end at that measurement. Infinity means not only that there will always be a measurement where the tortoise is ahead, it also means that there will always be an interval after the measurement where Achilles overtakes the velocity challenged reptile. In short, an infinite set means that the set always will extend beyond itself.

The physical allegory of the infinite set is a universe of stars and galaxies which expands into an infinity of empty space.  But can emptiness really envelope things or is it the expansion of things which exists on its own without any envelope? Is the assumption of empty space really a projection of our own intellectual expectations of set-making? I think that it is important to see that Einsteinian spacetime calculations would work the same either way. Spacetime need not be a literal container of mass-energy, if mass-energy is already entangled at superliminal rates. It makes it easy to think of General Relativity as referring to a spatiotemporal entity (a ‘reference mollusk’ as Einstein called it, or a Minkowski space), but the reality may be that spacetime is nothing more than the influence that the entangled consensus of mass-energetic relations has on itself. This way, no envelope of infinite emptiness is required around the Big Bang, and the vacuum can leave its quantum contents behind to revert to a true void. The vacuum energy gets turned inside out…it’s not inside of spacetime, it’s inside of relativity, i.e. universal perceptual entanglement.

Eastern and Western Eternity

If the Western view of time is an unlimited set of (limited) moments, then eternity is purely conceptual – the perpetually incomplete ‘set-hood’ of that set. The Western sense of eternity is also of perpetually filling itself with more and more clock ticks. Eastern mystics have promised instead that the fundamental truth of nature is the antithesis of that: A timeless connectedness of all things, or a universal connectability (The Force, Field, Love*, God) from which all ‘things’ are seemingly detached. Such a detachment is described as an illusion or temporary masking of underlying unity which remains eternal and pervasive. From the Eastern view, it is not space and time which contain all phenomena, but rather times and spaces are emergent dissociations within the grand phenomenality.

With the advent of General Relativity, the pendulum of Western thought began unknowingly to swing Eastward. Eternity came to be seen as a universal 4D manifold which distorts rates and lengths of physical processes. The distortions are understood to be relative to frames of reference; they are the ‘appearances’ of each frame to any other rather than a fixed physical property common to all frames. Frames themselves are, like the tortoise, given an unfair advantage of inheriting our ignorance of the nature of perception. Physics has attributed a frame-making capacity from a purely theoretical warrant, a warrant which magically acquires real powers of perceptual transformation (Lorentz contraction/dilation) which define the universe.

Some will complain that inertial or Galilean frames have nothing to do with perception, that they are tied only to linear velocity, however this takes velocity relations for granted in the same way that infinite sets take sets for granted. Here is where Relativity and QM completely agree. They both hinge on the concrete physical fact of measurement as the relation between properties such as space, time, position, and momentum. The measurement is a thing that separates the uncollapsed theoretical wave from the concrete wave-effects which are common to matter.

I submit that measurement itself is only the superficial way of understanding what is going on behind SR, GR, and QM. What makes measurement possible – all measurement – is an intrinsic relatability or sense which pervades all of physics. It is only parsimonious to assume at this point that this relatability is identical to the awareness which underlies our own conscious experience.

As it stands now, theoretical physics must resort to a kind of dualism where the idea of an ‘observer’ is somehow presumed separate from conscious observation. Any deviation from this premise is taboo and treated with antipathy. The Western imagination has been captured by positivism, so that all legitimate phenomena begin with an assumption of being separable from phenomenology. This unfortunately leaves phenomenology itself orphaned from physics, and the purest contents of conscious experience orphaned from legitimacy. We turn to the idea of “emergence” to reclaim some semblance of coherence, but emergence itself is no more physical or derivable from logic than consciousness itself.

Relativity applies to instantaneity as well as simultaneity.

To further bridge the Einsteinian notion of eternity with the Eastern one, I suggest a relativity of instantaneity. We can see from time lapse photography, for example, that different rates of exposure present nature at speeds of time. If we had nanobots we could surely step down our own body motions so that we could interact remotely with nanoscale objects at scales and speeds which would not be possible to us on the macro scale.

We can also see how the ocean appears to slow to a crawl when seen from the air. Interestingly, the trails that boats make in their wake appear to flow against a solid background of standing ocean waves.


In this photo you can’t see it, but next time you are flying over the water, notice how the narrow wake tracks which cross-cross the static ocean shimmer with movement. I’m curious about the physics of this – is it the distance of the plane or the speed which averages out the speed of water, and then the motion of the boat which makes some of the speed visible? Some kind of phase-cancellation?

It is this kind of transformation which I’m referring to as the relativity of instantaneity. The scope of the instant depends on perspective, and physics, having no preferred perspective, can have no way to define any separation between instants or any set which unites them. In this way, emergent properties themselves emerge from perception.

East vs West

I suspect that both views of time are reflections of the perspective from which they emerge. Eastern or Empathizing psychologies focus on the unity of categories in the category-making mind itself while Western, Systemizing modes focus on impersonal categories, the origin of which is seen as irrelevant. As the two modes have grown apart, they are no longer able to locate each other without distorting them into a straw man. The Western mind sees the Eastern view as an overestimation of our own presence (including the present moment) while the Eastern mind sees the fatal flaw of the Western effort to deflate the presence of the now and its presenter. Interestingly, the antipathy flips in the assignment of blame, with the Western skeptic taking personal umbrage at the individuals who they see as peddlers of ‘woo-woo’ superstition and postmodern ‘word salad’. By contrast, the Eastern mystic sees the Western resistance as a function of impersonal forces of spiritual immaturity. This dynamic of projection and inversion is a good place to study the lensing of consciousness. The model which I propose suggests that studying how people argue will show that fundamentalist positions on either side will have more in common with each other neurologically than there will be differences. From there we can begin to map the blind spot of the Western approach as it cascades down through academic policies, experiment design, and finally economics, and politics.

The Western approach is intrinsically bottom up in that it begins with a collection of external particulars and then extrapolates generalities and universal laws. Scientific thought is an analytic introspection which is intended to generate a synthetic ‘extraspection’. Our naive, introspective sense of the present time is as Edwin Schrodinger and Ken Wilber point out is “the only thing that has no end”. Meaning that we literally cannot locate within the present any beginning or ending. Only memories within the present which seem to explain things outside of the present can be found:

We dissipate our energies in fantasy mists of memories and expectations, and thus deprive the living present of its fundamental reality and reduce it to a “specious present”, a slender present that endures a mere one or two seconds, a pale shadow of the eternal Present.
-Ken Wilber, No Boundary

It seems clear to me that the Western view is dominated by the specific function of the intellect, which is to isolate problems and analyze them sequentially. Using the intellect to analyze itself, we conflate mental kinds of functions with nature in general and have learned to mistake this map of our own map-making for the territory. Because the Western mind identifies with itself rather than with the consciousness behind thought, it inverts our own existence into a ‘specious presence’. First an orphaned soul in an Enlightened machine, then a self-modeling semantic mechanism, the personal presence has now been so aggressively deflated that many insist that it has no existence at all.

If the Western view overlooks the magnitude of significance of the present in its modeling of time, the Eastern view overlooks the overwhelming influence of non-human scales of the present in the universe. The human scale of ‘now’ is overly preferred, so that the Western half of the universe, with its bottom up chains of causality, can be discounted irrationally (hence the woo-woo). This means that the vital and important contributions of science and technology can be dismissed by the Eastern approach, thus losing all credibility with Western thinkers. The sentiment that thoughts create reality is straw-manned to imply that human thoughts create all reality, when the truth is that human influence may be both more powerful and less powerful than we imagine.

Coming Together Over Time

I propose that the way to transcend the problematic notions of time in both the Western and Eastern modes is to see time as the “most common sense” through which eternity ‘pretends’ to be each moment, and how the eternal moment pretends to its own eachness. Time is what limits the unlimited and opens the limited to the possibility of the infinite.

Because the Western view of time has resulted in an all-but-insignificant present, it has contrived an all-but insignificant subjective conscious presence to act as an almost-disposable timekeeper. The ‘observer’ in physics is naught but a convergence of particular coordinates…coordinates which themselves are only defined by there own axiomatic coordination. The cosmos appears as an unorchestrated orchestration…an autoverse rather than universe.

The Eastern view inflates the present and the subjective presence to the absolute extreme, so that the cosmos appears as an unfalsifiably teleological monolith. This infuriates the Western mind, hearing soft-headed homilies of ‘There are no coincidences’ and ‘Everything happens for a reason’ to justify pre-scientific superstition. This would be a solipseverse rather than a universe – a universe which fits into single self. Monotheism splits the difference, with a Unisolipse – a single God self who is not us, but who is like us and can help us and care about us.

What I propose is that each of these models fall out naturally as reflections from a sense-based foundation. The true universe is an orchestration of (orchestration-unorchestration) of perceived qualities and conditions. A paratheistic or ambitheistic society of self-elaborating experiences.

*Love to me seems more human-centric or mammal-centric to me, but I think that Love could be better understood in this context as the most recent form of empathy or sense. Sense allows wholes and parts to partially disconnect and reconnect with the whole.

  1. November 13, 2015 at 11:09 am

    I am not sure that any interval less than the Planck time (10**-43 seconds) has any meaning.
    The science geek

    • November 13, 2015 at 11:17 pm

      I tend to agree. I suppose there could always be some new level of ‘dark electromagnetism’ discovered that would open up sub-Planck scales, but 10^-43 is small enough for me.

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